LEADER 04636nam 22007095 450 001 9910480715803321 005 20200706022631.0 010 $a3-642-57951-5 024 7 $a10.1007/978-3-642-57951-6 035 $a(CKB)3400000000104358 035 $a(SSID)ssj0000805847 035 $a(PQKBManifestationID)11458114 035 $a(PQKBTitleCode)TC0000805847 035 $a(PQKBWorkID)10841528 035 $a(PQKB)11774836 035 $a(DE-He213)978-3-642-57951-6 035 $a(MiAaPQ)EBC3089646 035 $a(PPN)23791946X 035 $a(EXLCZ)993400000000104358 100 $a20121227d1994 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential Forms and Applications$b[electronic resource] /$fby Manfredo P. Do Carmo 205 $a1st ed. 1994. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1994. 215 $a1 online resource (X, 118 p.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-57618-5 320 $aIncludes bibliographical references (page 115) and index. 327 $a1. Differential Forms in Rn -- 2. Line Integrals -- 3. Differentiable Manifolds -- 4. Integration on Manifolds; Stokes Theorem and Poincaré?s Lemma -- 1. Integration of Differential Forms -- 2. Stokes Theorem -- 3. Poincaré?s Lemma -- 5. Differential Geometry of Surfaces -- 1. The Structure Equations of Rn -- 2. Surfaces in R3 -- 3. Intrinsic Geometry of Surfaces -- 6. The Theorem of Gauss-Bonnet and the Theorem of Morse -- 1. The Theorem of Gauss-Bonnet -- 2. The Theorem of Morse -- References. 330 $aThis is a free translation of a set of notes published originally in Portuguese in 1971. They were translated for a course in the College of Differential Geome­ try, ICTP, Trieste, 1989. In the English translation we omitted a chapter on the Frobenius theorem and an appendix on the nonexistence of a complete hyperbolic plane in euclidean 3-space (Hilbert's theorem). For the present edition, we introduced a chapter on line integrals. In Chapter 1 we introduce the differential forms in Rn. We only assume an elementary knowledge of calculus, and the chapter can be used as a basis for a course on differential forms for "users" of Mathematics. In Chapter 2 we start integrating differential forms of degree one along curves in Rn. This already allows some applications of the ideas of Chapter 1. This material is not used in the rest of the book. In Chapter 3 we present the basic notions of differentiable manifolds. It is useful (but not essential) that the reader be familiar with the notion of a regular surface in R3. In Chapter 4 we introduce the notion of manifold with boundary and prove Stokes theorem and Poincare's lemma. Starting from this basic material, we could follow any of the possi­ ble routes for applications: Topology, Differential Geometry, Mechanics, Lie Groups, etc. We have chosen Differential Geometry. For simplicity, we re­ stricted ourselves to surfaces. 410 0$aUniversitext,$x0172-5939 606 $aDifferential geometry 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aMathematical physics 606 $aPhysics 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 615 0$aDifferential geometry. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aMathematical physics. 615 0$aPhysics. 615 14$aDifferential Geometry. 615 24$aAnalysis. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aMathematical Methods in Physics. 615 24$aNumerical and Computational Physics, Simulation. 676 $a515/.37 700 $aDo Carmo$b Manfredo P$4aut$4http://id.loc.gov/vocabulary/relators/aut$0912565 906 $aBOOK 912 $a9910480715803321 996 $aDifferential Forms and Applications$92043853 997 $aUNINA